The ratio of work done (W) to the amount of heat produced (Q) is always a constant, represented by J.
i.e., W J
Q
where J is called Joule's mechanical equivalent of heat. The value of
J = 4.186 joule/calorie.
If temperature of a body of mass m rises by T, then Q = mc T where
c is specific heat of the material of the body,
When the state of body of mass m changes at its melting point/boiling point, then Q = m L, where L is latent heat of the body.
All solids expand on heating. The coefficient of linear expansion ( ), coefficient of superficial expansion () and coefficient of cubical expansion () are related as
2 3
.
In case of liquids, r = a + c where r is coefficient of real expansion of a liquid, a is coefficient of apparent expansion of the liquid and r is coefficient of cubical expansion of the vessel.
Principle of calorimetry : When two substances at different temperatures are mixed together, they exchange heat. If we assume that no heat is lost to the surroundings, then according to principle of calorimetry.
by on subs tan ce by another substance
Specific heat of gases : Specific heat of a gas is the amount of heat required to raise the temperature of one gram of gas through 1°C.
Principal specific heat of a gas :
(i) Specific heat at constant volume (cv) (ii) Specific heat at constant pressure (cp)
Cv molar heat capacity at constant volume Cp molar heat capacity at constant pressure
Cp – CV = R/J
Coefficient of thermal conductivity (K) of a solid conductor is calculated from the relation
Q T KA t t
where A is area of hot face, x is distance between the hot and cold faces, Q is the small amount of heat conducted in a small time (t), T is difference in temperatures of hot and cold faces.
Here (T/x) temperature gradient, i.e., rate of fall of temperature with distance in the direction of flow of heat.
All liquids and gases are heated by convection. Heat comes to us from the sun by radiation.
Newton's Law of Cooling : It states that the rate of loss of heat of a liquid is directly proportional to difference in temperatures of the liquid and the surroundings provided the temperature difference is small (= 30°C).
0
dQ T T dt or dQ K T
T0
dt As,
0
dQ ms dT K T T dt dt or
0
dT T T dt . When the temperature difference between body and surroundings is large, then Stefan's law for cooling of body is obeyed. According to it,
E = (T4 T 04)
where E is the amount of thermal energy emitted per second per unit area of a black body. T is the temperature of black body and T0 is the temperature of surroundings, is the Stefan's constant.
Wien's Displacement Law : The wavelength max at which the maximum amount of energy is radiated decreases with the increase of temperature and is such that
maxT = a constant
where T is the temperature of black body in Kelvin.
Thermodynamical system : An assembly of extremely large number of gas molecules is called a thermodynamical system. The pressure P, volume
V, temperature T and heat cotent Q are called Thermodynamical parameters.
Zeroth Law of Thermodynamics : (Concept of temperature) According to this law, when thermodynamic systems A and B are separately in thermal equilibrium with a third thermodynamic system C, then the systems A and
B are in thermal equilibrium with each other also.
Internal Energy of a Gas is the sum of kinetic energy and the potential energy of the molecules of the gas.
K.E./molecule 1 23
2mc 2k T where k is Boltzmann's constant. internal energy of an ideal gas is wholly kinetic.
First Law of Thermodynamics (principle of conservation of energy) According to this law dQ = dU + dW
where dQ is the small amount of heat energy exchange with a system, dU is small change in internal energy of the system and dW is the small external work done by or on the system.
Sign conventions used in thermodynamics.
(a) Heat absorbed by the system = positive and heat rejected by the system = negative.
(b) When temperature of the system rises, its internal energy increases U = positive.
When temperature of the system falls, its internal energy decreases, U = negative.
(c) When a gas expands, work is done by the system. It is taken as positive. When a gas is compressed, work is done on the system. It is taken as negative.
Isothermal changes Adiabatic changes
Temperature (T) remains constant, i.e., 1. Heat content and entropy are constant,
T = 0 i.e., Q = const ; S = constant, Q = 0;
S = 0
Changes are slow. 2. Changes are fast.
System is thermally conducting. 3. System is thermally insulated.
Internal energy, U = constant U = 0 4. Internal energy changes, i.e., U 0
Specific heat, c = 5. Specific heat, c = 0
Equation of isothermal changes, 6. Eqn. of adiabatic changes
PV = constant. (i) PV = constant (ii) TV –1 = constant
(iii) P1 – T = constant P V T , U1 1 T , U2 2 T > T2 1; U > U2 1 P V T1 T > T2 1 T2
Slope of isothermal curve, dP P
dV V
7. Slope of adiabatic curve, dP P
dV V
Coeff, of isothermal elasticity, Ki = P 8. Coeff. of adiabatic elasticity, Ka = P
Work done in isothermal expansion 9. Work done in adiabatic expansion
W = 2.303 nRT log10 (V2/V1) 2 1 1 nR T T W n number of mole W = 2.303 P1 V1 log10 (V2/V1) P V2 21 PV1 1 W = 2.303 nRT log10 (P1/P2) W = C (T1 – T2)
Second Law of Thermodynamics : It is impossible for self acting machine, unaided by an external agency to convey heat from the body at lower temperature to another at higher temperature. This statement of the law was made by Clausius.
According to Kelvin, it is impossible to derive a continuous supply of work by cooling a body to a temperature lower than that of the coldest of its surroundings.
Heat Engines : A heat engine is a device which converts heat energy into mechanical energy. Efficiency of a heat engine is the ratio of work done (W) by the engine per cycle to the energy absorbed from the source (Q1) per cycle. 1 2 2 1 1 1 1 Q Q Q W
Q Q Q where Q2 = heat rejected to the sink
Carnot Engine : is an ideal heat engine which is based on Carnot's
reversible cycle. Its working consists of four steps. (Isothermal expansion, Adiabatic expansion isothermal compression and adiabatic compression).
The efficiency of Carnot engine is given by 2 2
1 1
1 Q 1 T
Q T
where Q1 is heat energy absorbed from the source maintained at high temperature T1K and Q2 is amount of heat energy rejected to the sink at low temperature T2K.
A Refrigerator absorbs heat Q2 from a sink (substance to be cooled) at lower temperature TK. Electric energy W has to be supplied for this purpose
Q1 = Q2 + W
Coefficient of performance (b) of a refrigerator is the ratio of the heat
absorbed per cycle from the sink (Q2) to the electric energy supplied (W) for this purpose per cycle, i.e.,
Q2, W i.e., 2 2 1 2 1 2 1 Q T Q Q T T
QUESTIONS
1. Why spark is produced when two substances are struck hard against each other?
2. What is the specific heat of a gas in an isothermal process. 3. On what factors, does the efficiency of Carnot engine depend? 4. What are two essential features of Carnot's ideal heat engine.
5. Plot a graph between internal energy U and Temperature (T) of an ideal gas.
6. Refrigerator transfers heat from cold body to a hot body. Does this violate the second law of thermodynamics.
7. What is heat pump?
8. Give two example of heat pump? 9. What is heat engine?
10. Why a gas is cooled when expanded?
11. Can the temperature of an isolated system change?
12. Which one a solid, a liquid or a gas of the same mass and at the same temperature has the greatest internal energy.
13. Under what ideal condition the efficiency of a Carnot engine be 100%. 14. Which thermodynamic variable is defined by the first law of thermo-
dynamics?
15. Give an example where heat be added to a system without increasing its temperature.
16. What is the efficiency of carnot engine working between ice point and steam point?
17. Two blocks of the same metal having masses 5g and 10g collide against a target with the same velocity. If the total energy used in heating the balls which will attain higher temperature?
18. What is the specific heat of a gas in an adiabatic process.